Separable Gaussian Filtering

2D Gaussian filter는 Separable 하기 때문에

이를 이용하면 다음과 같이 연산량을 줄일 수 있다.

n addition to being circularly symmetric, the Gaussian blur can be applied to a two-dimensional image as two independent one-dimensional calculations, and so is termed separable. That is, the effect of applying the two-dimensional matrix can also be achieved by applying a series of single-dimensional Gaussian matrices in the horizontal direction, then repeating the process in the vertical direction. In computational terms, this is a useful property, since the calculation can be performed in  time (where his height and w is width; see Big O notation), as opposed to  for a non-separable kernel.

출처 : http://en.wikipedia.org/wiki/Gaussian_blur

반면 Laplacian은 non-separable하기 때문에 연산량이 많다.

이는 LoG를 DoG로 approximation 하는 이유이기도 하다.

출처 : http://math.stackexchange.com/questions/132183/laplacian-2d-kernel-is-it-separable

Log -> DoG approximation 참고

http://www.cse.psu.edu/~rcollins/CSE486/lecture11_6pp.pdf

http://en.wikipedia.org/wiki/Laplacian_of_Gaussian#The_Laplacian_of_Gaussian

http://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf

http://blog.naver.com/PostView.nhn?blogId=aik1919&logNo=140068508527

http://dong3640.com.ne.kr/laboratory/imageprocessing/2nd-Log.htm

http://fourier.eng.hmc.edu/e161/lectures/gradient/node10.html

http://homepages.inf.ed.ac.uk/rbf/HIPR2/log.htm